A search for the Higgs boson decaying into a pair of charm quarks is presented. The analysis uses proton- proton collisions to target the production of a Higgs boson in association with a leptonically decaying W or Z boson. The dataset delivered by the LHC at a centre-of-mass energy of root s = 13 TeV and recorded by the ATLAS detector corresponds to an integrated luminosity of 139 fb(-1). Flavour-tagging algorithms are used to identify jets originating from the hadronisation of charm quarks. The analysis method is validated with the simultaneous measurement of WW, WZ and ZZ production, with observed (expected) significances of 2.6 (2.2) standard deviations above the background-only prediction for the (W/Z)Z(-> c